$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 6x + 5$ and $ BC = 3x + 32$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {6x + 5} = {3x + 32}$ Solve for $x$ $ 3x = 27$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 6({9}) + 5$ $ BC = 3({9}) + 32$ $ AB = 54 + 5$ $ BC = 27 + 32$ $ AB = 59$ $ BC = 59$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {59} + {59}$ $ AC = 118$